It follows the discovery of five bodies in four cars in the Stavropol region. All victims had been shot dead.
Local police said when investigators approached one of the vehicles, an improvised explosive device went off close by, but that no-one was injured.
Police have reportedly released the names and photos of three suspects.
Another explosive device was made safe. Security forces are on high alert.
The Russian authorities have already tightened security in the Black Sea resort of Sochi to ensure that next month`s Olympics are safe.
`Islamist group`
Two of the victims have been identified as local taxi drivers and all four cars are said to be Ladas, which are commonly used as cabs in Russia.
All of the victims were found in Stavropol`s Kirovsky and Predgorny districts on Wednesday, Russia`s lenta.ru news website reports.
According to the Russian news website Life News, which has close links to the security forces, three suspects from the neighbouring region of Kabardino-Balkaria are being sought by police.
Two of the men named are already on a Russian federal wanted list for the murder of a hunter last year. and are said to be members of an Islamist militant group.
About 37,000 police and interior ministry troops are now in place to provide security for the Games, which open on 7 February, Russian officials say.
The main concern is the threat of attack by Islamist militants from the restive North Caucasus region.
Russia`s most wanted man, Chechen rebel leader Doku Umarov, has urged his fighters to target the Winter Games.
Security fears have been heightened after two suicide bomb attacks killed 34 people in the southern city of Volgograd on 29 and 30 December.
Investigators believe the perpetrators were two men who arrived in the city from the North Caucasus region.
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